By the "gulf coast" you mean heading north along the east side of the mountains obviously , but where are you starting this section?
From the Yucatan at Campeche it is a simple matter of getting on Mex 180 and rthat gets you to Brownsvile Texas. It will be a simple matter of following the 180 signs , sometimes on sandbar coast strip like thru Cd,del Carmen . flat banana/cacao/sugarcane/coconut plantation country in Tabasco, wetlands. and some neat green low volcanic mountains around Santiago Tuxtla ,Veracruz, then green hills and citrus, more sugarcane Tampico and flat farm and ranchlands and chaparral to Texas. You will only see the Gulf on the first sandbar stretch , and on the Costa Esmeralda. Rest of route is inland a bit.
For variety you could go still farther inland . take Mex 145 from Sayula to Tuxtepec and Cordoba- more hilly , ranches and major pineapple growing zone .
Gas available all over the place, inexpensive hotels too.
Really there are lots of possible variants , just pick a road, go , enjoy